As of now, on the page move screen in the new editer, the search button on the parent page is a drop-down.
This drop-down button makes it difficult to understand that users can intentionally enter text and search, so I would recommend improving the UI.

 

 Suggested solution

In the page move screen, as in the legacy editor, "Search" and "Recently viewed" should be separated, and the "Search" screen should be changed to a search field.